NAG AD Library
f11jc (real_symm_solve_ichol)

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1 Purpose

f11jc is the AD Library version of the primal routine f11jcf. Based (in the C++ interface) on overload resolution, f11jc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine f11jc_AD_f ( method, n, nnz, a, la, irow, icol, ipiv, istr, b, tol, maxitn, x, rnorm, itn, work, lwork, ifail)
Integer, Intent (In) :: n, nnz, la, irow(la), icol(la), istr(n+1), maxitn, lwork
Integer, Intent (Inout) :: ipiv(n), ifail
Integer, Intent (Out) :: itn
ADTYPE, Intent (In) :: a(la), b(n), tol
ADTYPE, Intent (Inout) :: x(n)
ADTYPE, Intent (Out) :: rnorm, work(lwork)
Character (*), Intent (In) :: method
Type (c_ptr), Intent (Inout) :: ad_handle
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
when ADTYPE is Real(kind=nag_wp) then AD is p0w
when ADTYPE is Type(nagad_a1w_w_rtype) then AD is a1w
when ADTYPE is Type(nagad_t1w_w_rtype) then AD is t1w
C++ Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void f11jc ( handle_t &ad_handle, const char *method, const Integer &n, const Integer &nnz, const ADTYPE a[], const Integer &la, const Integer irow[], const Integer icol[], Integer ipiv[], const Integer istr[], const ADTYPE b[], const ADTYPE &tol, const Integer &maxitn, ADTYPE x[], ADTYPE &rnorm, Integer &itn, ADTYPE work[], const Integer &lwork, Integer &ifail)
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f11jc is the AD Library version of the primal routine f11jcf.
f11jcf solves a real sparse symmetric system of linear equations, represented in symmetric coordinate storage format, using a conjugate gradient or Lanczos method, with incomplete Cholesky preconditioning. For further information see Section 3 in the documentation for f11jcf.

4 References

Barrett R, Berry M, Chan T F, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C and Van der Vorst H (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods SIAM, Philadelphia
Meijerink J and Van der Vorst H (1977) An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix Math. Comput. 31 148–162
Paige C C and Saunders M A (1975) Solution of sparse indefinite systems of linear equations SIAM J. Numer. Anal. 12 617–629
Salvini S A and Shaw G J (1995) An evaluation of new NAG Library solvers for large sparse symmetric linear systems NAG Technical Report TR1/95

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11jc includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine. A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
1: ad_handlenag::ad::handle_t Input/Output
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: method – character Input
3: n – Integer Input
4: nnz – Integer Input
5: a(la) – ADTYPE array Input
6: la – Integer Input
7: irow(la) – Integer array Input
8: icol(la) – Integer array Input
9: ipiv(n) – Integer array Input
10: istr(n+1) – Integer array Input
11: b(n) – ADTYPE array Input
12: tolADTYPE Input
13: maxitn – Integer Input
14: x(n) – ADTYPE array Input/Output
Please consult Overwriting of Inputs in the NAG AD Library Introduction.
15: rnormADTYPE Output
16: itn – Integer Output
17: work(lwork) – ADTYPE array Workspace
18: lwork – Integer Input
19: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11jc preserves all error codes from f11jcf and in addition can return:
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.
The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11jc is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for f11jcf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example solves a symmetric positive definite system of equations using the conjugate gradient method, with incomplete Cholesky preconditioning.

10.1 Adjoint modes

Language Source File Data Results
Fortran f11jc_a1w_fe.f90 f11jc_a1w_fe.d f11jc_a1w_fe.r
C++ f11jc_a1w_hcppe.cpp f11jc_a1w_hcppe.d f11jc_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran f11jc_t1w_fe.f90 f11jc_t1w_fe.d f11jc_t1w_fe.r
C++ f11jc_t1w_hcppe.cpp f11jc_t1w_hcppe.d f11jc_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran f11jc_p0w_fe.f90 f11jc_p0w_fe.d f11jc_p0w_fe.r
C++ f11jc_p0w_hcppe.cpp f11jc_p0w_hcppe.d f11jc_p0w_hcppe.r